$Q$-dependent electronic excitations in osmium: Pressure- and temperature-induced effects

Raman scattering by electrons and phonons has been studied in single crystals of the $5d$ transition-metal osmium under pressures up to 60 GPa in the temperature range of 10–300 K. An anomalous increase in the electronic light-scattering cross section was found in the pressure range of 20–30 GPa with the use of green and blue excitation wavelengths. At these conditions, we observe an appearance of well-defined electronic peaks at $\sim 580{\text{cm}}^{-1}$ for the wave-vector direction $\mathbf{q}\parallel \left[0001\right]$ and at $\sim 350{\text{cm}}^{-1}$ for $\mathbf{q}\parallel \left[10\overline{1}0\right]$. The comparison of $\mathbf{q}$ dependencies measured and calculated from the first-principles spectra suggests a strong volume- and temperature-dependent renormalization of the energies and damping of the electronic states near the Fermi level.

Figure 1

Raman spectra at different pressures (GPa) measured from the (0001) plane at (a) $T=10$ and (b) 300 K, $E_i=2.41\text{eV}$.

Figure 2

Raman spectra at different pressures (GPa) measured from $\left(10\overline{1}0\right)$ plane at (a) $T=10$ and (b) 300 K, $E_i=2.41\text{eV}$.

Figure 3

The ELS peak intensity vs pressure for both $\mathbf{q}$ directions (after subtraction of low-pressure structureless background intensity), $T=10\text{K}$, and $E_i=2.41\text{eV}$.

Figure 4

The wave-vector distributions ${\left|U\left(q\right)\right|}^2$ for different incident energies. The expression is given in Sec. 4.

Figure 5

The measured for $\mathbf{q}\parallel \left[0001\right]$ high and low-pressure Raman spectra and the calculated ELS spectra (50 GPa) for different excitation energies, $T=10\text{K}$. (a) $E_i=2.41\text{eV}$ (514 nm), (b) $E_i=1.96\text{eV}$ (633 nm), and (c) $E_i=1.68\text{eV}$ (740 nm).

Figure 6

The measured (taken from Ref. 21) and calculated (solid lines are nonresonant case and dashed lines are resonant) ELS spectra for both $\mathbf{q}$ directions and different polarization geometries. $E_i=1.83\text{eV}$, $P=0\text{GPa}$, and $T=10\text{K}$. The vertical line marks the position of the ELS spectra with $\mathbf{q}\parallel \left[0001\right]$.

Figure 7

(Color online) The measured and calculated [from Eq. (1)] ELS high and ambient pressure spectra for (a) $\mathbf{q}\parallel \left[0001\right]$ and (b) $\mathbf{q}\parallel \left[10\overline{1}0\right]$. $T=10\text{K}$ and $E_i=2.41\text{eV}$. The calculated intensities were normalized to the measured ones. The calculated FS is shown in the inset.

Figure 8

The measured (points) and calculated (dashed lines at 0 GPa and solid lines at 50 GPa) ELS maxima positions vs $E_i$ for (a) $\mathbf{q}\parallel \left[10\overline{1}0\right]$ and (b) $\mathbf{q}\parallel \left[0001\right]$, where $T=10\text{K}$.

Figure 9

(Color online) Band structure obtained within the LDA approach with spin-orbit coupling with $+u$ (red, solid) and $-u$ (green, dashed) distortions in the $X$ direction. Fermi level corresponds to zero energy.

Figure 10

(Color online) Band structure obtained within the LDA approach with spin-orbit coupling for $P=50\text{GPa}$ with $+u$ (red, solid) and $-u$ (green, dashed) distortions in the $X$ direction. Fermi level corresponds to zero energy.